COMP30019 Graphics and Interaction Illumination Models Adrian - - PowerPoint PPT Presentation

COMP30019 Graphics and Interaction Illumination Models

Adrian Pearce

Department of Computer Science and Software Engineering University of Melbourne

The University of Melbourne

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

Lecture outline

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

Introduction to illumination

How does light interact with object surfaces? Aim: understand illumination models and surface properties for realistic shading. Reading:

◮ Foley Sections 14.1 Illumination models.

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

Shading and illumination

In real scenes, there is a variation of shading over object surfaces caused by

◮ surface material properties, ◮ orientation of surfaces, ◮ nature and direction of light sources, ◮ view direction and ◮ shadows.

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

Surface types

In order to create realistic renderings by computer graphics, we need to attempt to simulate this shading for different kinds of surfaces:

◮ self-luminous, ◮ transparent refractive, ◮ transparent translucent, ◮ reflective, ◮ diffuse (also body reflection or matte ), ◮ specular (aka surface reflection or gloss), ◮ textured (macrotexture versus microtexture).

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

Surface examples

◮ Self lunious example is some kinds of jelly fish that glow in

dark or radioactive isotopes

◮ Transparent refractive, – glass or water ◮ Transparent translucent – light interacts in more complex

way, e.g scatters.

◮ reflection, either

◮ diffuse (body reflection), e.g. carpet ◮ specular (surface reflection), e.g. polished steel.

◮ These shading patterns can provide useful perceptual

clues about the 3D structure of the scene.

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

Isotropic surfaces

In isotropic surfaces the relationship between the incoming (or incident) and outgoing (or reflected) direction of light is the same over the whole surface (otherwise anisotropic). Illumination models generally most often consider isotropic surfaces only, however:

◮ Certain kinds of material (such as velour) and certain rock

• r stone faces (look different depending on angle that you

view them).

◮ As a result of asymmetric microtexture.

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

Shading model versus illumination model

There is a difference between the shading model and the illumination model used in rendering scenes,

◮ the illumination model captures how light sources interacts

with object surfaces, and

◮ the shading model determines how to render the faces of

each polygon in the scene. The shading model depends on illumination model, for example

◮ some shading models invoke an illumination model for

every pixel (such as ray tracing),

◮ others only use the illumination model for some pixels and

the shade the remaining pixels by interpolation (such as Gouraud shading).

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

◮ The illumination model is about determining how light

sources interacts with object surfaces

◮ Whereas the shading model is about how to interpolate

• ver the faces of polygons, given the illumination.

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

The choice of illumination model will generally be a compromise between modelling the physics fully, and the computational cost.

◮ Simple illumination models do not consider shadows,

reflections or photon-based effects (such as radiosity).

◮ In full ray tracing one considers all rays of light and their

recursive interaction between each object —very computationally complex!

◮ In limit can’t model exactly since (ray tracing is

undecidable: not Turing computable), so have to make decision about model limitations no matter what, e.g. how many time will we recurse (in other words how many times will we allow for re-reflection) ?

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

Ambient illumination

The simplest kind of shading is that from ambient illumination, that is, light that comes uniformly from all directions. The radiated light intensity I at a point on a surface depends on the intensity of the illumination Ia, and on the reflectivity ka (or albedo) of the surface—the fraction of the incoming light which the object reflects, near zero for black objects, near one for white objects. Thus I = Iaka Ambient illumination is mathematically an extended form of Lambertian reflection, integrating contributions from an infinite number of infinitesimal point light sources in all directions, instead of a single point light source.

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

In ambient shading assume that light comes uniformly from all directions (average of full rendering case).

◮ Involves integrating contributions from an infinite number of

infinitesimal point light sources in all directions.

◮ Radiated light intensity I at a point on a surface depends

• n the intensity of illumination Ia and reflectivity, or albedo,
• f the surface ka.

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

Diffuse (Lambertian) reflection

When a ray of light hits a surface, some fraction of it penetrates some way into the body of the object, where it is scattered (and may interact with coloured pigment particles). Eventually, some

• f the light is reradiated more-or-less uniformly in all directions.

For a given surface, the brightness depends only on the angle θ between the direction ¯ L to the light source and the surface normal ¯ N (Foley Figure 14.01).

θ N L

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

◮ The brightness depends only on the angle θ between the

direction ¯ L to the light source and the surface normal ¯ N.

◮ This is the so-called Lambertian reflection (or matte, or

diffuse or body reflection—all these terms are used.)

◮ In Lambertian reflection light is re-radiated uniformly in all

directions.

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

We assume that the light source is a point, so that over a tiny patch of surface, all the incident light rays are effectively

• parallel. (This will be approximated, in practice, by a small light

source, like a light globe, which is reasonably far away.) The intensity of light re-radiated from a tiny patch of surface depends on the intensity Ip of the incoming light from the point light source, on how much of this light is intercepted by the surface patch, and on the reflectivity kd (or albedo) of the surface. If the surface patch is facing full-on to the light source, then it will intercept the maximum amount of light. As the patch turns away from the light, it will intercept less of the light, following a cosine law, cos θ, where θ is the angle between the local surface normal, and the direction to the light source.

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

The diffuse (or Lambertian) illumination equation is therefore I = Ipkdcosθ This cosine can be expressed as a scalar product, thus the Lambertian contribution to the total intensity is I = Ipkd( ¯ N · ¯ L) where ¯ L and ¯ N are unit vectors in the directions, respectively, of the light source and of the surface normal.

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

Independence of surface orientation

For a given small surface patch, the amount of light radiated towards the viewer is greatest when the surface normal is pointing straight at the viewer, and falls off according to a cosine law as the surface slants away from the viewer. However, at the same time, for a given visual angle subtended at the viewer, more of the surface is seen within that angle as the surface slants away from the viewer, again according to a cosine law. These two effects exactly compensate, so, overall, Lambertian reflection is independent of surface orientation with respect to the viewer.

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

Light beam shown in 2D cross-section (Foley Figure 14.02).

dA 90−θ dA cos θ θ N Surface 1 Surface 2 N

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

◮ At angle of incidence of θ, less light is radiated towards the

viewer, according to I = Ipkdcosθ, however,

◮ a greater are is intercepted according to dA cosθ.

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

Independence of distance of viewer from surface

Likewise, as the surface moves further away from the viewer, the received light intensity falls off as an inverse-square law in distance. However, for a given angle subtended at the viewer, the amount

• f surface included grows in proportion to the square of the

distance. These two effects also compensate, so that intensity of Lambertian reflection is independent of the distance of the surface from the viewer.

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

Dependence of distance of light source from surface

The intensity of the incoming light (and therefore of the reflected light) does depend on the distance of the surface from the light source. Physically, for a point light source, this dies off in inverse proportion to the square of the distance. However, if this physical law is followed in rendering, the intensity seems to go down unrealistically fast. (This is probably because most real lighting is not from a single, ideal point source.)

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

Dependence of distance of light source from surface

Therefore, many graphics systems use a factor of the form 1 C + U where U is the light-source distance, and C is some constant

• ffset. This is ad-hoc, but gives reasonable results.

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

If the light source is sufficiently “distant”, then all parts of the

• bject can be regarded as equally far from the light source, and

therefore no such correction need be made. The effect of distance, the same for all points, can essentially be absorbed into the light-source intensity factor Ip.

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

Specular reflection

When a ray of light hits a surface, some fraction of it is also reflected immediately at the outer boundary of the surface. This is the specular reflection and leads to highlights and glossiness. If the surface were a perfect mirror, then the reflection would follow the law of perfect reflection: For an incident ray of light from the light source, the emergent reflected ray would lie in the plane defined by the incident ray and the surface normal, and make the same angle with the surface normal as the incident ray. (This direction of perfect reflection can be derived using a little vector geometry.)

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

For most glossy surfaces, however, the reflected light is spread

• ut (e.g. scratches in steel of texture in plastic), to a greater or

lesser degree, from the direction of perfect reflection. This is caused by microscopic unevenness of the surface: there are a lot of little reflecting facets, whose normals vary from the overall surface normal. The reflection is strongest in the direction of perfect reflection, and becomes weaker for directions away from this.

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

Specular reflection as a function of angle

This spread of reflection can be modelled in a number of different ways. Most common is to look at the angle α between the direction of perfect reflection and the viewer direction, and modify the reflected intensity by the factor (cos α)n (Foley Figure 14.08).

θ θ α N V R L

(cosα)n is at its maximum, 1, when the viewer direction coincides with the direction of perfect reflection, and becomes less for directions away from this.

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

Specular reflection exponent

The exponent n is the specular reflection exponent and controls the degree of spread.

◮ High values of n (maybe as much as 100 or 200) lead to a

rapid fall-off and sharp highlights, corresponding to a very glossy surface, almost like a mirror.

◮ Low values (as low as 1 or 2) lead to a slow fall-off and

spread-out, more diffuse highlights, a more matte surface appearance.

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

◮ High values of specular reflection exponent correspond to

very glossy surfaces, such as Steel.

◮ Low values of specular reflection exponent correspond to

very glossy surfaces, such as carpet.

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

Specular reflection is independent of material colour

Notice that specular reflection, being from the outer surface, does not involve interaction with the body of the material, and so is independent of Lambertian reflectivity. This is particularly important in dealing with colour. The colour of a specular reflection depends only on the colour

• f the incoming light, not on the colour of the material.

Example: coloured reflections on surface of steel.

◮ The colour of a specular reflection depends only on the

colour of the incoming light, not on the colour of the material.

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

Phong illumination model and specular reflection

Iλ = IaλkaOdλ + fattIpλ[kdOdλcosθ + W(θ)cosnα] Iλ = IaλkaOdλ + fattIpλ[kdOdλ( ¯ N.¯ L) + ks(¯

• R. ¯

V)n] where Iaλ is the ambient light (as a function of wavelength), Ipλ is the point light source, Odλ is objects diffuse colour, W(θ) is the fraction of specularly reflected light, kd is the diffuse-reflection coefficient, ks is the specular reflection coefficient, n is the specular-reflection exponent and fatt is the light source attenuation factor (a function of distance).

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

θ θ α N V R L

(Foley Figure 14.08)

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

Phong developed this popular model in 1975 — assures a maximum specular reflection occurs when α is zero and falls off sharply as α increases.

◮ Need to first identify that amount of incident light specularly

reflected depends on the angle of incidence θ.

◮ If W(θ) is the fraction of specularly reflected light, then

Phong’s model is (point to the first equation in the slide).

◮ Note that W(θ) is equivalent to ks, the specular reflection

coefficient (W(θ) is set to a constant ks, the mateiral’s specular-reflection coefficient which ranges between 0 and 1).

◮ Then point out that if the direction of reflection ¯

R and the viewpoint direction ¯ V are normalised, then cosα = ¯

• R. ¯

V.

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

Spheres shaded using Phong’s illumination model for increasing values of n (higher specular reflection exponent from left to right) and ks (higher specular reflectivity coefficient, albedo, from top to bottom) (Foley Figure 14.10).

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

Combined lighting models

The combination of the above three components, ambient illumination, Lambertian reflection, and (simple) specular reflection is adequate to give reasonably realistic renderings. In certain circumstances, greater realism can be achieved (at greater computation cost), by taking into account how the fraction of incident light reflected (versus what enters the body

• f the surface) depends somewhat on the angle of incidence.

This is governed by the Fresnel equation. There are also effects of incident or reflected light being blocked by small-scale surface roughness. However, these effects can usually be ignored.

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

Lambertian (top) versus Lambertian and ambient (bottom)

(Foley Figures 14.03 and 14.04).

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

The mixing of ambient reflection (light from all directions) with Lambertian (light from a point light source) can lead to reasonably realistic effects.

◮ Ambient light is a bit like averaging all rays coming from all

directions together with a dominant source.

◮ This example corresponds to something rather like

Styrofoam balls from a bean bag.

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

Multiple Light Sources

If there are multiple light sources, then their contributions at any point on a surface add together, less any shadowing.

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models

Summary

◮ Lambertian surfaces exhibit body reflection (or

re-radiation), independent of orientation and distance from viewer but not light source, leading to matte appearance.

◮ Specular surfaces exhibit surface reflection, dependent on

• rientation and distance of both viewer and light source,

leading to glossy appearance with highlights.

◮ The Phong illumination model captures a combination

surface properties including

◮ diffuse (Lambertian with point light source), ◮ ambient (special case of Lambertian with uniform light), and ◮ specular reflection

as a function of wavelength.

Adrian Pearce University of Melbourne COMP30019 Graphics and InteractionIllumination Models